# Common Multiples

• In mathematics, factors are those numbers which divide another number completely without leaving the remainder i.e. with zero remainder.
• Also, by multiplying the two or more factors we will get another number also, the number which we will get after multiplying the factors of the number is called as the multiple.

For example:

12 can be written as,     12 = 1*12

12 = 3*4

12 = 6*2

Thus, here 1, 2, 3, 4, 6 and 12 are the factors of 12.

While 12 is the multiple of 1, 2, 3, 4, 6 and 12. Thus, the relationship between factors and multiple is given by,

Multiple = Factor* Factor

## Common multiples:

The common multiples are the numbers which are common to two or more than two list of multiples.

And the smallest common multiple is called as the least common multiple.

For example:

We see that, the numbers we get in the table of 2 are all the multiples of 2 because they are the results of multiplication of other numbers which is explained as follows. We see that, the numbers we get in the table of 3 are all the multiples of 3 because they are the results of multiplication of other numbers which is explained as follows. Thus, from the table of 2 and 3 we see that, there are some multiples which are in the list of both the multiples i.e. multiple of 2 as well as 3 also.

These multiples which are common to multiples of 2 and 3 are:

6, 12, 18, 24 and 30, hence these are the common multiples of 2 and 3.

And 6 is the least common multiple of 2 and 3.

For example if we have to find the common multiples of 3, 4 and 6 up to 30.

Then first we write the multiples of 3, 4 and 5 separately up to 30 as follows.

And then we common out the numbers from multiples of 3, 4 and 6.

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30.

The multiples of 4 are: 4, 8, 12, 16, 20, 24, and 28.

The multiples of 6 are: 6, 12, 18, 24 and 30.

Thus, the common multiples of 3, 4 and 6 are: 12 and 24

And 12 is the least common multiple of 3, 4 and 6.

For example if we have to find the common multiples of 5 and 10 up to 50.

Then first we write the multiples of 5 and 10 separately. And then we common out the multiples from the multiples of 5 and 10 as follows.

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50

The multiples of 10 are: 10, 20, 30, 40, and 50.

Thus, the common multiples of 5 and 10 are: 10, 20, 30, 40 and 50.

And 10 is the least common multiple of 5 and 10.

Updated: July 15, 2021 — 11:11 pm